The presented method describes reflection and transmission of electromagnetic waves at multiple closely stacked metal grids using multi-modal S-parameter propagation. For that, the surface admittance of every metal layer was determined, through a novel semi-analytic approach that uses simple Fourier transformations instead of solving an integral equation. The modal components of this surface admittance were used to express the generalized scattering matrices of the individual grids. By applying multi-modal propagation techniques to the resulting scattering parameters, it was possible to model the electromagnetic interactions within a multilayer stack of periodic impedance sheets. Resulting reflection and transmission parameters perfectly matched the corresponding full-wave simulations even above the grating lobe regime. In the end, the universality of the proposed method was proven on a layer stack, connected to lumped components.